Exploratory Analysis: FPCA for PFT other Conifers with disturbances between 2015 and 2040

Patches which face a disturbance between the years 2015 and 2040 are the basis for this analysis. As a first step in the exploratory analysis, the data is represented as functions by means of a b-spline basis equivalently as for PFT Tundra, i.e. b-splines of order 6, penalizing the third derivative with a penalization parameter \(\lambda = 1\).

Basis Representation - other Conifers

Figure 1 shows the chosen basis representation for other Conifers.

Figure 1: Smoothed basis representation for PFT other Conifers and all four scenarios.
Figure 1: Smoothed basis representation for PFT other Conifers and all four scenarios.

Principal Component Analysis - other Conifers

To further analyze the data, a FPCA is run for each of the four scenarios and each of the five PFTs separately. Again, let’s take a look at the two principal components for each scenario of PFT other Conifers. Figure 2 shows the principal components.

Figure 2: First two principal components for each scenario for PFT other Conifers
Figure 2: First two principal components for each scenario for PFT other Conifers

For Tundra, we could see huge differences between the Control scenario and the climate scenario. Here however, the first principal components for all four scenarios are pretty similar and all reflect the same patterns: high values in the first PC stand for much higher values of above ground carbon than the mean after the 10 first years of the considered time span and vice versa for low values. The second principal component mainly reflects lower values as the mean for higher PC2 scores until a break point and then higher values than the mean, vice versa for lower values of PC2. Note that the time point of the change differs among the scenarios and that this effect is reversed for the control scenario!

With VARIMAX rotation

For a better understanding and an easier interpretation of the principal components, a VARIMAX rotation is applied. This rotation algorithm may reveal more meaningful components of variation in the data (Ramsay et al. (2009)).

Figure 3 shows the VARIMAX rotated first and second principal components for each scenario.

Figure 3: First two principal components for each scenario for PFT other Conifers with VARIMAX rotation.
Figure 3: First two principal components for each scenario for PFT other Conifers with VARIMAX rotation.

Here, an interesting development is present: for the control and the SSP1-RSP2.6 scenario the first component nearly stays unchanged with only small changes at the end of the time span. For the two more drastic scenarios however, the first principal component covers now a shift with high PC2 values indicating a higher share than the mean until the year 2060 and a smaller share in the remaining time (and vice versa for lower PC2 values). For the second principal component, mainly the crossing point changes in comparison to the unrotated one.

Cluster detection: PC1 vs. PC2 - other Conifers

In order to detect possible clusters in the data, i.e. the share of above ground carbon may behave in similar ways for several grid points, the two first principal components are plotted against each other for all considered cases: unrotated (Figure 4) and VARIMAX rotated (Figure 5). The color reflects a rough classifying into regions, here continents.

Figure 4: First principal component vs. second principal component for each scenario for PFT other Conifers.
Figure 4: First principal component vs. second principal component for each scenario for PFT other Conifers.

In Figure 4, no clear clustering pattern is visible. In total, the scores are rather similar among all scenarios.

Figure 5: First VARIMAX rotated component vs. second VARIMAX rotated component for each scenario for PFT other Conifers
Figure 5: First VARIMAX rotated component vs. second VARIMAX rotated component for each scenario for PFT other Conifers

Rotation does not lead to a substantial difference in PC scores for other Conifers. This was already indicated in Figure 3 as the PCs hardly change in comparison to the unrotated ones.

Spatial Distribution visualized in world maps

In order to get a better understanding of the spatial component of the data, Figure 6 shows how the portion of above ground carbon from year 0 to 100 after disturbance develop in each grid cell (patch 1).

Figure 6: Spatial distribution of the portion of above ground carbon after distrubance for each scenario for PFT Other Conifers.
Figure 6: Spatial distribution of the portion of above ground carbon after distrubance for each scenario for PFT Other Conifers.

We can clearly see smaller differences between the scenarios and the considered regions. The more drastic the warming scenario, the less other Conifers is present.